Self-organization of a critical state and 1/f fluctuations caused by the interaction of phase transitions in a distributed system

A mathematical model is proposed that describes the appearance of fluctuations with a spectral density inversely proportional to the frequency as a result of the intersection of phase transitions in a spatially inhomogeneous system. The model is represented by a set of two nonlinear stochastic differential equations with mutually interacting order parameters. It is demonstrated that a random walk in the model potential field corresponding to the intersecting sub-and supercritical phase transitions may lead to the self-organization of a critical state and the appearance of fluctuations with a 1/f spectral density.